Glossary
10% Condition
A condition used when sampling without replacement, stating that the sample size (n) must be less than 10% of the population size (N) to ensure approximate independence of trials.
Example:
When drawing 5 cards from a deck of 52 without replacement, the 10% Condition (5 < 0.10 * 52 = 5.2) is met, allowing us to treat the draws as approximately independent for binomial calculations.
Binary (Condition)
One of the BINS conditions for a binomial distribution, requiring that each trial has only two possible outcomes: success or failure.
Example:
In a survey asking if a student passed or failed a test, the outcome for each student is Binary.
Binomial Distribution
A probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes and the probability of success is constant.
Example:
When a basketball player shoots 10 free throws, the number of shots they make can be modeled by a Binomial Distribution, assuming each shot is independent and has the same probability of going in.
Failure
The other possible outcome in a binomial trial, representing any outcome that is not a success.
Example:
If we define getting a '6' on a die roll as a success, then rolling any other number (1, 2, 3, 4, or 5) is a Failure.
Independent (Condition)
One of the BINS conditions for a binomial distribution, requiring that the outcome of one trial does not affect the outcome of any other trial.
Example:
When flipping a fair coin multiple times, each flip is Independent of the previous ones; getting heads on one flip doesn't change the probability of getting heads on the next.
Mean (Expected Value) of Binomial Variable
The average number of successes expected in a binomial distribution, calculated as the number of trials (n) multiplied by the probability of success (p).
Example:
If a baseball player has a 0.300 batting average and gets 100 at-bats, the Mean (Expected Value) of hits is 100 * 0.30 = 30 hits.
Number (Condition)
One of the BINS conditions for a binomial distribution, requiring that the number of trials (n) is fixed in advance.
Example:
If you decide to roll a die exactly 20 times, the Number of trials is fixed at 20.
Same Probability (Condition)
One of the BINS conditions for a binomial distribution, requiring that the probability of success (p) remains constant for every trial.
Example:
For a quality control check where 5% of items are defective, the Same Probability of 0.05 applies to each item inspected.
Standard Deviation of Binomial Variable
A measure of the typical variability or spread of the number of successes around the mean in a binomial distribution, calculated as $\sqrt{n * p * (1-p)}$.
Example:
For a binomial distribution with n=100 and p=0.5, the Standard Deviation of Binomial Variable is , indicating typical variation around the mean of 50.
Success
One of the two possible outcomes in a binomial trial, representing the event of interest that we are counting.
Example:
In a coin flip experiment, if we are counting heads, then getting a head is considered a Success.
Trial
A single observation or instance in a series of repetitions, where each instance has two possible outcomes (success or failure).
Example:
Each individual question answered on a multiple-choice quiz can be considered a Trial if we're counting correct answers.